Problem: Simplify the following expression: $ a = \dfrac{-5}{3} - \dfrac{-4k}{k - 3} $
Explanation: In order to subtract expressions, they must have a common denominator. Multiply the first expression by $\dfrac{k - 3}{k - 3}$ $ \dfrac{-5}{3} \times \dfrac{k - 3}{k - 3} = \dfrac{-5k + 15}{3k - 9} $ Multiply the second expression by $\dfrac{3}{3}$ $ \dfrac{-4k}{k - 3} \times \dfrac{3}{3} = \dfrac{-12k}{3k - 9} $ Therefore $ a = \dfrac{-5k + 15}{3k - 9} - \dfrac{-12k}{3k - 9} $ Now the expressions have the same denominator we can simply subtract the numerators: $a = \dfrac{-5k + 15 + 12k }{3k - 9} $ Distribute the negative sign: $a = \dfrac{-5k + 15 + 12k}{3k - 9}$ $a = \dfrac{7k + 15}{3k - 9}$